Industrial chemical plants often operate under strict data confidentiality constraints, making centralized data-driven process modeling difficult. Federated learning (FL) provides a promising solution by enabling collaborative model training across distributed facilities without sharing raw operational data. This paper proposes a privacy-preserving federated learning framework for distributed chemical process optimization using data collected from multiple geographically separated plants. Each plant locally trains a neural-network-based process model using its own time-series sensor data, while only model parameters are transmitted to a central aggregation server through secure aggregation mechanisms. This design allows cross-plant knowledge sharing while maintaining strict data locality and industrial confidentiality. Experimental evaluation was conducted using process datasets from three independent chemical plants operating under heterogeneous conditions. The results demonstrate rapid convergence of the federated model, with the global mean squared error decreasing from approximately 2369 to below 50 within the first five communication rounds and stabilizing around 35 after 40 rounds. In comparison with local-only training, the proposed federated framework significantly improves prediction accuracy across all plants, while achieving performance comparable to centralized training. The findings indicate that federated learning provides an effective and scalable solution for collaborative industrial analytics, enabling privacy-preserving predictive modeling and process optimization across distributed chemical production facilities.